From Lesson 7 : Gradients and Color Spaces

3. Applying Sobels

import numpy as np
import cv2
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import pickle


# Read in an image and grayscale it
image = mpimg.imread('signs_vehicles_xygrad.png')

# Define a function that applies Sobel x or y, 
# then takes an absolute value and applies a threshold.
# Note: calling your function with orient='x', thresh_min=20, thresh_max=100
# should produce output like the example image shown above this quiz.
def abs_sobel_thresh(img, orient='x', sobel_kernel=3, thresh=(0,255)):
    
    # Apply the following steps to img
    # 1) Convert to grayscale
    gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
    # 2) Take the derivative in x or y given orient = 'x' or 'y'
    if orient == 'x' :
        sobelResult = cv2.Sobel(gray, cv2.CV_64F, 1, 0,ksize=sobel_kernel)
    if orient == 'y' :  
        sobelResult = cv2.Sobel(gray, cv2.CV_64F, 0, 1,ksize=sobel_kernel)
    # 3) Take the absolute value of the derivative or gradient
    abs_sobel = np.absolute(sobelResult)
    # 4) Scale to 8-bit (0 - 255) then convert to type = np.uint8
    scaled_sobel = np.uint8(255*abs_sobel/np.max(abs_sobel))
    # 5) Create a mask of 1's where the scaled gradient magnitude 
            # is > thresh_min and < thresh_max
    binary_output = np.zeros_like(scaled_sobel)
    binary_output[(scaled_sobel > thresh[0]) & (scaled_sobel < thresh[1])] = 1
    # 6) Return this mask as your binary_output image
    #binary_output = np.copy(img) # Remove this line
    return binary_output
    
# Run the function
#grad_binary = abs_sobel_thresh(image, orient='x', sobel_kernel=3, thresh_min=20, thresh_max=100)
grad_binary = abs_sobel_thresh(image, orient='y', sobel_kernel=3, thresh=(20,100))
# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(24, 9))
f.tight_layout()
ax1.imshow(image)
ax1.set_title('Original Image', fontsize=50)
ax2.imshow(grad_binary, cmap='gray')
ax2.set_title('Thresholded Gradient', fontsize=50)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)

4. Magnitude of the gradient

import numpy as np
import cv2
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import pickle


# Read in an image
image = mpimg.imread('signs_vehicles_xygrad.png')

# Define a function that applies Sobel x and y, 
# then computes the magnitude of the gradient
# and applies a threshold
def mag_thresh(img, sobel_kernel=3, mag_thresh=(0, 255)):
    
    # Apply the following steps to img
    # 1) Convert to grayscale
    gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
    # 2) Take the gradient in x and y separately
    sobelx = cv2.Sobel(gray, cv2.CV_64F, 1, 0,ksize=sobel_kernel)
    sobely = cv2.Sobel(gray, cv2.CV_64F, 0, 1,ksize=sobel_kernel)
    # 3) Calculate the magnitude 
    abs_sobel = np.sqrt((sobelx**2) + (sobely**2))
    # 4) Scale to 8-bit (0 - 255) and convert to type = np.uint8
    scaled_sobel = np.uint8(255*abs_sobel/np.max(abs_sobel))
    # 5) Create a binary mask where mag thresholds are met
    binary_output = np.zeros_like(scaled_sobel)
    binary_output[(scaled_sobel > mag_thresh[0]) & (scaled_sobel < mag_thresh[1])] = 1
    # 6) Return this mask as your binary_output image
    #binary_output = np.copy(img) # Remove this line
    return binary_output
    
# Run the function
#mag_binary = mag_thresh(image, sobel_kernel=9, mag_thresh=(30, 100))
mag_binary = mag_thresh(image, sobel_kernel=9, mag_thresh=(80, 100))

# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(24, 9))
f.tight_layout()
ax1.imshow(image)
ax1.set_title('Original Image', fontsize=50)
ax2.imshow(mag_binary, cmap='gray')
ax2.set_title('Thresholded Magnitude', fontsize=50)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)

5. Direction of the Gradient

import numpy as np
import cv2
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import pickle


# Read in an image
image = mpimg.imread('signs_vehicles_xygrad.png')

# Define a function that applies Sobel x and y, 
# then computes the direction of the gradient
# and applies a threshold.
def dir_threshold(img, sobel_kernel=3, thresh=(0, np.pi/2)):
    
    # Apply the following steps to img
    # 1) Convert to grayscale
    gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
    # 2) Take the gradient in x and y separately
    sobelx = cv2.Sobel(gray, cv2.CV_64F, 1, 0,ksize=sobel_kernel)
    sobely = cv2.Sobel(gray, cv2.CV_64F, 0, 1,ksize=sobel_kernel)
    # 3) Take the absolute value of the x and y gradients
    abs_sobelx = np.absolute(sobelx)
    abs_sobely = np.absolute(sobely)
    # 4) Use np.arctan2(abs_sobely, abs_sobelx) to calculate the direction of the gradient
    direction = np.arctan2(abs_sobely,abs_sobelx)
    # 5) Create a binary mask where direction thresholds are met
    binary_output = np.zeros_like(direction)
    binary_output[(direction > thresh[0]) & (direction < thresh[1])] = 1
    # 6) Return this mask as your binary_output image
    #binary_output = np.copy(img) # Remove this line
    return binary_output
    
# Run the function
#dir_binary = dir_threshold(image, sobel_kernel=15, thresh=(0.7, 1.3))
dir_binary = dir_threshold(image, sobel_kernel=15, thresh=(.7, 1.3))
# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(24, 9))
f.tight_layout()
ax1.imshow(image)
ax1.set_title('Original Image', fontsize=50)
ax2.imshow(dir_binary, cmap='gray')
ax2.set_title('Thresholded Grad. Dir.', fontsize=50)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)

6. Combining thresholds

If you play around with the thresholds in the last exercise, you'll find that you can start to identify the lane lines by gradient direction alone by setting the threshold around thresh = (0.7, 1.3), but there's still a lot of noise in the resulting image.

Now consider how you can use various aspects of your gradient measurements (x, y, magnitude, direction) to isolate lane-line pixels. Specifically, think about how you can use thresholds of the x and y gradients, the overall gradient magnitude, and the gradient direction to focus on pixels that are likely to be part of the lane lines.

Challenge:

In the project at the end of this section, you'll want to experiment with thresholding various aspects of the gradient, so now would be a great time to start coding it up on your local machine! Grab the image we've been working with for the last three quizzes here (or a smaller jpg file here).

Combine the selection thresholds from the last 3 quizzes to write a piece of code like the following, where you can play with various thresholds and see the output.

Try different combinations and see what you get.

For example, here is a selection for pixels where both the xx and yy gradients meet the threshold criteria, or the gradient magnitude and direction are both within their threshold values.

combined = np.zeros_like(dir_binary)
combined[((gradx == 1) & (grady == 1)) | ((mag_binary == 1) & (dir_binary == 1))] = 1

# Choose a Sobel kernel size
ksize = 15 #3 # Choose a larger odd number to smooth gradient measurements

# Apply each of the thresholding functions
gradx = abs_sobel_thresh(image, orient='x', sobel_kernel=ksize, thresh=(20, 100))
grady = abs_sobel_thresh(image, orient='y', sobel_kernel=ksize, thresh=(20, 100))
mag_binary = mag_thresh(image, sobel_kernel=ksize, mag_thresh=(30, 100))
dir_binary = dir_threshold(image, sobel_kernel=ksize, thresh=(0.7, 1.3))

combined = np.zeros_like(dir_binary)
combined[((gradx == 1) & (grady == 1)) | ((mag_binary == 1) & (dir_binary == 1))] = 1

# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(24, 9))
f.tight_layout()
ax1.imshow(image)
ax1.set_title('Original Image', fontsize=50)
ax2.imshow(combined, cmap='gray')
ax2.set_title('Thresholded Grad. Dir.', fontsize=50)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)